Shuffle quadri-algebra and concatenation

TL;DR

This paper explores the algebraic structure of shuffle quadri-algebras, establishing relations between key algebraic operations and demonstrating module-algebra structures within the shuffle algebra.

Contribution

It introduces new relations between shuffle product, concatenation, and deconcatenation, and shows the shuffle algebra has two module-algebra structures.

Findings

Established relations between quadri-algebra laws

Proved the existence of module-algebra structures

Enhanced understanding of shuffle algebra properties

Abstract

In this article, we study the shuffle quadri-algebra H. We prove the existence of some relations between quadri-algebra laws which constitute shuffle product, the concatenation product and the deconcatenation coproduct. We also show that the underlying shuffle algebra has two module-algebra structures on itself.